Ajax PHP Frameworks

These libraries are comprised of a JavaScript part for the browser side, and PHP scripts working on the server.
Here is a list of the main open source solutions among which some are part of this Comparison of web frameworks. Sources of the tests are provided.

The highest figures, the number of requests per second, are the best test results.The faster framework are for the Go or Python languages. The fastest PHP framework is Code Igniter.
These tests are not significant actually because it is access to databases that slow down the most applications and displaying a "Hello World!" message is not sufficient to evaluate a tool, particularly because  PHP has a high startup time while  other tools work differently, staying active between successive launches of the application.

Ajax and PHP frameworks

They are all compatible with PHP 5.

Prado Symfony Tigermouse

Laravel

PHP only frameworks

Such pure PHP framework may be completed by a JavaScript Ajax framework but it is not part of it.

Code Igniter CakePHP FuelPHP Photon

reactPHP

See also...

HTML 5 frameworks. They work on the client side but provide greater interactivity with the server.